When drilling a new borehole or a sidetrack in an existing well, the drilling head may drill into a low pressure zone, resulting in a loss of pressure. Thus, the mud entered into the hole while drilling to prevent blowout is lost in the low pressure zone, and there will be a substantial risk of a blowout if the drilling is continued. Cementing and thus sealing part of the annulus above the low pressure zone are also impossible, since the injected cement is lost as it disappears into the low pressure zone, and then this partly drilled borehole is abandoned and plugged from above and a new well is drilled.